scholarly journals Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 719 ◽  
Author(s):  
Shahid Mahmood ◽  
Nusrat Raza ◽  
Eman S. A. AbuJarad ◽  
Gautam Srivastava ◽  
H. M. Srivastava ◽  
...  
Keyword(s):  
Integral Operator ◽  
Bessel Function ◽  
Analytic Functions ◽  
Operator Coefficient ◽  
Geometric Properties ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Inclusion Relations

This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order γ ( γ ∈ C \ 0 ) . This introduced a q-integral operator and certain subclasses of the newly introduced classes are defined by using this q-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the ( δ , q )-neighborhood of analytic functions are introduced and the inclusion relations between the ( δ , q )-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed.

scholarly journals Coefficient Bounds for Certain Subclasses of Analytic Functions Defined by Komatu Integral Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Serap Bulut
Keyword(s):  
Differential Equation ◽  
Integral Operator ◽  
Analytic Functions ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Type Differential Equation

We determine the coeffcient bounds for functions in certain subclasses of analytic functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy–Euler type differential equation of orderm. Relevant connections of some of the results obtained with those in earlier works are also provided.

scholarly journals Coefficients estimates of some subclasses of analytic functions related with conic domain

2013 ◽  
Vol 21 (2) ◽  
pp. 181-188 ◽  
Author(s):  
Sarfraz Nawaz Malik ◽  
Mohsan Raza ◽  
Muhammad Arif ◽  
Saqib Hussain
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Coefficient Bounds ◽  
Conic Domain

Abstract In this paper, the authors determine the coefficient bounds for functions in certain subclasses of analytic functions related with the conic regions, which are introduced by using the concept of bounded boundary and bounded radius rotations. The effect of certain integral operator on these classes has also been examined.

scholarly journals Geometric Properties of a New Integral Operator

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Roberta Bucur ◽  
Loriana Andrei ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties ◽  
Special Cases

We obtain sufficient conditions for the univalence, starlikeness, and convexity of a new integral operator defined on the space of normalized analytic functions in the open unit disk. Some subordination results for the new integral operator are also given. Several corollaries follow as special cases.

scholarly journals Convolution properties for subclasses of meromorphic univalent functions of complex order

Filomat ◽  
2012 ◽  
Vol 26 (1) ◽  
pp. 153-163 ◽  
Author(s):  
Teodor Bulboacă ◽  
Mohamed Aouf ◽  
Rabha El-Ashwah
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Complex Order ◽  
Inclusion Relations ◽  
Coefficient Inequalities ◽  
Convolution Properties ◽  
Meromorphic Univalent Functions

Using the new linear operator Lm(?,l)f(z) = 1/z + ??k=1(l/l+ ?k)m akzk-1, f ? ?, where l > 0, ? ? 0, and m ? N0 = N ? {0}, we introduce two subclasses of meromorphic analytic functions, and we investigate several convolution properties, coefficient inequalities, and inclusion relations for these classes.

scholarly journals Inclusion and neighborhood properties of a certain subclasses of p-valent functions with negative coefficients

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 1-13 ◽  
Author(s):  
R.M. El-Ashwah
Keyword(s):  
Differential Equation ◽  
Analytic Functions ◽  
Function Class ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Inclusion Relations

By means of Ruscheweyh derivative operator, we introduced and investigated two new subclasses of p-valent analytic functions. The various results obtained here for each of these function class include coefficient bounds and distortion inequalities, associated inclusion relations for the (n, ?)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of non-homogenous differential equation.

scholarly journals Neighborhoods of Certain Multivalently Analytic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Serap Bulut
Keyword(s):  
Analytic Functions ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Function Classes ◽  
Convolution Structure

We introduce and investigate two new general subclasses of multivalently analytic functions of complex order by making use of the familiar convolution structure of analytic functions. Among the various results obtained here for each of these function classes, we derive the coefficient bounds, distortion inequalities, and other interesting properties and characteristics for functions belonging to the classes introduced here.

scholarly journals ON NEW CLASSES OF ANALYTIC FUNCTIONS IMPOSED VIA THE FRACTIONAL ENTROPY INTEGRAL OPERATOR

2017 ◽  
pp. 293 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Tsallis Entropy ◽  
Complex Domain ◽  
Schwarz Function ◽  
Geometric Properties ◽  
Fractional Entropy ◽  
Euler Form

In this paper, we aim to introduce some geometric properties of analytic functions by utilizing the concept of fractional entropy in a complex domain. We extend the fractional entropy, type Tsallis entropy in the complex z-plane, by using some analytic functions. Established by this diffusion,we state specic new classes of analytic functions (type Schwarz function). Other geometric properties are validated in the sequel. Our development is completed by the Euler form Lemma and Jack Lemma.

Geometric properties of the differential shift plus complex Volterra operator

2017 ◽  
Vol 11 (01) ◽  
pp. 1850013
Author(s):  
Rabha W. ibrahim
Keyword(s):  
Hardy Space ◽  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Volterra Operator ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties

In this paper, we define a new integral operator in the open unit disk. This operator is considered as a complex Volterra operator. Moreover, we define a new subspace of Hardy space involving the normalized analytic functions. We shall show that the new integral operator is closed in the subspace of normalized functions. Geometric characterizations are established in the sequel. Our display is maintained by the Jack Lemma.

scholarly journals Certain Subclasses of Analytic Functions with Complex Order

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
A. Selvam ◽  
P. Sooriya Kala ◽  
N. Marikkannan
Keyword(s):  
Analytic Functions ◽  
Coefficient Bounds ◽  
Complex Order

Two new subclasses of analytic functions of complex order are introduced. Apart from establishing coefficient bounds for these classes, we establish inclusion relationships involving (n-δ) neighborhoods of analytic functions with negative coefficients belonging to these subclasses.

scholarly journals Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator

2021 ◽  
pp. 49-76
Author(s):  
Faroze Ahmad Malik ◽  
Nusrat Ahmed Dar ◽  
Chitaranjan Sharma
Keyword(s):  
Convex Functions ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Extreme Points ◽  
Integral Operators ◽  
Integral Means ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Special Cases ◽  
The Family

We use the concept of convolution to introduce and study the properties of a unified family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$, $(0\leq\gamma\leq1,\,k\geq0)$, consisting of uniformly $k$-starlike and $k$-convex functions of complex order $b\in\mathbb{C}\setminus\{0\}$ and type $\alpha\in[0,1)$. The family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$ is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman's conjecture for integral means inequality. Moreover, invariance of this family under certain well-known integral operators is also established in this paper. Some previously known results are obtained as special cases.

Sign in / Sign up

Export Citation Format

Share Document